New Hampshire’s stay-at-home order will likely extend past early May, Gov. Chris Sununu said Thursday, as the latest test numbers show no sign that the rate of new COVID-19 infections has slowed.

“Are we going to continue the stay-at-home order beyond May 4? In some fashion, it’s very likely, yes,” Sununu said at a news conference. “It’s not just going to go away on May 5. I can’t foresee that right now because we’re just not going to have the data to support that.”

Sununu said a task force he convened this week, made up of state officials and business leaders, will begin to craft recommendations for how different industries can safely resume operations whenever the time comes. And the state may be able to offer some flexibility to certain sectors, like health care, as a first step.

But generally, he said, the state will keep most restrictions in place until it sees a sustained decrease in the rate of new infections — which is not happening yet.

At the same news conference, state health officials announced 84 new positive tests for COVID-19, including the first in Gilsum. This followed Wednesday’s announcement of 99 new confirmed cases — the highest one-day increase so far in New Hampshire.

Dr. Benjamin Chan, the state epidemiologist, said officials believe the daily tallies have grown compared to a week ago because of increased testing, not because the virus is spreading more rapidly.

“We do not believe that we’re seeing an increase in overall community transmission,” he said. “We also, however, have not seen yet a decrease in the numbers.”

The state reported results from 797 tests Thursday and 971 tests Wednesday. Last week, it was averaging closer to 400 tests per day, according to N.H. Department of Health and Human Services data.

Chan said the most effective way to prevent the spread of the virus right now is continued social distancing. He urged people to stay home as much as possible and, when out, to keep a six-foot distance from others and wear a cloth mask or face covering.

A total of 1,670 Granite Staters have tested positive for COVID-19 to date.

On Thursday, the state health department also reported three additional deaths related to COVID-19. They were all men, age 60 or older, and lived in Hillsborough, Rockingham and Strafford counties.

Chan said all three deaths were associated with institutional outbreaks.

At least eight New Hampshire long-term care facilities have experienced coronavirus outbreaks, according to state health officials. The only one in the Monadnock Region to date is Crotched Mountain in Greenfield, which serves people with disabilities and has had one announced death.

Health and Human Services Commissioner Lori Shibinette announced outbreaks at two more facilities Thursday, both in Derry: Pleasant Valley Nursing Home and Derry Health and Rehab.

Thirty of the state’s 51 deaths so far have been associated with outbreaks at such facilities, Chan said.

Of the new COVID-19 cases announced Thursday, two were Cheshire County residents, including the Gilsum result.

Locally, COVID-19 has also been confirmed in Acworth, Alstead, Antrim, Bennington, Chesterfield, Fitzwilliam, Greenfield, Harrisville, Hillsboro, Hinsdale, Jaffrey, Keene, Marlborough, New Ipswich, Peterborough, Rindge, Swanzey, Temple, Washington and Westmoreland.

Hillsborough County, outside of Manchester and Nashua, had 11 more cases confirmed Thursday, while Sullivan County had none.

At Thursday’s news conference, Sununu said that while the reopening task force does not have any public health experts, its recommendations will go to state health officials with that expertise.

“Everything will be run through the department of public health because that has to be the preeminent concern,” he said.

He said the state will work to allow whatever flexibility it can, consistent with public health.

“We’re looking at hospitals, we’re looking at some of the other business sectors where we think it might be easier to get them up and running,” he said. “It doesn’t mean they’re going to be up and running on May 5, necessarily.”

Some industries will likely reopen sooner than others, he added.

Facing the possibility that the virus may circulate for months — or longer, Sununu said Granite Staters shouldn’t expect an immediate return to normalcy, even when he begins to relax restrictions.

“We are likely in this for quite some time, but we’re trying to develop these new models of normal so that society can go on,” he said. “… The point is to try to get to a point where we’re not just reacting to the crisis, but truly managing through it. And that allows us to have a little more flexibility in our lives and workplaces.”

Paul Cuno-Booth can be reached at 352-1234, extension 1409, or Follow him on Twitter @PCunoBoothKS